Given a set (actually an array) and a symmetric relation (actually a boolean function), this divides the set into the equivalence classes of the reflexive and transitive closure of the relation.

eq_classes.js

function eq_classes(set, rel) {
  var classes = {}, connected_stack, root,
    stack_top, elt, pushed_more;

  while(set.length > 0) {
    root = set.shift();
    classes[root] = [root];
    connected_stack = [root];

    while(connected_stack.length > 0) {
      stack_top = connected_stack[connected_stack.length - 1];
      pushed_more = false;
      for(elt in set) {
        if(rel(stack_top, set[elt])) {
          pushed_more = true;
          connected_stack.push(set[elt]);
          classes[root].push(set[elt]);
          set.splice(elt, 1);
        }
      }
      if(!pushed_more) {
        connected_stack.pop();
      }
    }
  }
  return classes;
}